Community detection in complex networks has attracted considerable attention, however, most existing methods need the number of communities to be specified beforehand. In this paper, a goodness-of-fit test based on the linear spectral statistic of the centered and rescaled adjacency matrix for the stochastic block model is proposed. We prove that the proposed test statistic converges in distribution to the standard Gaussian distribution under the null hypothesis. The proof uses some recent advances in generalized Wigner matrices. Simulations and real data examples show that our proposed test statistic performs well. This paper extends the work of Dong et al. [Information Science 512 (2020) 1360-1371].

翻译：复杂网络中的社区检测引起了广泛关注，然而现有大多数方法需要预先指定社区数量。本文提出了一种基于中心化与重新缩放邻接矩阵的线性谱统计量的随机块模型拟合优度检验方法。我们证明了在原假设下，所提出的检验统计量依分布收敛于标准高斯分布。该证明利用了广义Wigner矩阵的最新进展。模拟实验和真实数据分析表明，所提出的检验统计量表现良好。本文扩展了Dong等人[Information Science 512 (2020) 1360-1371]的研究工作。